The present invention relates generally to the heating of loads located within opaque metal foils and containers provided with at least one overlayer containing microwave absorbing material, and certain semi-transparent materials, and particularly to a product that automatically provides time dependent heating of such loads using thermalization of microwave energy by the absorbing material as the primary source of heat.
In U.S. application Ser. No. 670,008 by Fabish et al, filed Mar. 15, 1991, now U.S. Pat. No. 5,258,596, issued Nov. 2, 1993, a system is described that uses microwave reflection, absorption and transmission coefficients attainable with commercially available lossy materials to describe the thermal response of a load to an arbitrary influx of microwave power. Material parameters employed in the system are complex numbers defined by real and imaginary terms that describe the relative magnetic permeability and electric permittivity of the lossy materials at the electromagnetic frequency of interest. The disclosure of the Fabish et al application is incorporated herein by reference.
Heretofore, one practice employed to control cooking time and temperature in thermalizing microwave energy in lossy materials was to use magnetic components having specific Curie temperatures that lay near the maximum desired temperature. Upon approach to the Curie temperature, the magnetic order disappears and heat generation ceases. Such a concept is disclosed in U.S. Pat. No. 2,830,162 to Copson et al and used generally in U.S. Pat. No. 4,266,108 to Anderson et al. In Anderson et al., the thickness of the lossy material is critical and, in addition, rather large so that commercialization of such means is limited.
U.S. Pat. Nos. 4,864,089 and 4,876,423 to Tighe et al show microwave heating mediums for liquid application to microwave transparent substrates. Because the substrate and any containers made therefrom are generally semi-transparent to microwave radiation, the load beneath the substrate or in the container is heated directly by the microwave energy as well as the heat of any thermalization of the radiation within the heating mediums.
The various absorber designs appearing in the literature can be fruitfully discussed within the framework of Maxwell's equations. It is worthwhile to outline here one solution in some detail that is pertinent to understanding the semi-transparent absorber. (A metal-backed absorber is similarly disclosed and discussed in the above incorporated Fabish et al. application.)
A drawing of a suitable model for this purpose is shown in FIG. 1. The model comprises a semi-transparent polymer film 2 of thickness d.sub.2 and intrinsic impedance z.sub.2, which is adjacent to free space on its left, the free space having an intrinsic impedance z.sub.0 (=377.OMEGA.). A second polymer film 3 is located on the right of film 2, film 3 having a thickness d.sub.3 and an intrinsic impedance z.sub.3. Free space is also located to the right of film 3. The bar over the z denotes a complex quantity.
z.sub.L is the impedance of the combination of films 2 and 3 exposed to a normally incident microwave power, P.sub.I, and is given by the following equations: ##EQU1## The definitions of the terms in Equations 1 to 8 are given below and on pages 18 to 21 of the above incorporated Fabish et al. application. Equations 2 through 8 enable calculation of power absorption P.sub.A under boundary conditions that generally represent packaging applications using transparent and semi-transparent materials, namely, lossless and lossy dielectric materials, respectively. The results of the calculation permit a meaningful comparison with the performance of the D-layer disclosed in the above Fabish et al. application and shown in FIG. 2 of the drawing in the present application.
The metal-backed absorber (D-layer) discussed in the above incorporated Fabish et al. application is attained from FIG. 1 by letting material 3 become a metal of sufficient thickness to prevent any power transmission through its thickness d.sub.3. The case where the metal is a perfect conductor and the transverse electromagnetic wave (TEM) is normally incident on a semi-infinite planar surfaces (FIG. 2) described by: EQU z/z.sub.0 =[K.sub.m /K.sub.e ].sup.1/2 tanh.GAMMA.d (9)
where for all cases in Equations 1 to 9:
the bars denote a complex quantity; PA1 z=E/H is the (complex) impedance of the films or D-layer; PA1 z.sub.0 =[.mu..sub.o .epsilon..sub.o ].sup.1/2 is the characteristic impedance of free space, where .mu..sub.o and .epsilon..sub.o are the permeability and permittivity of free space, respectively, and PA1 z.sub.0 =377.OMEGA. in the MKS system of units (an unoccupied oven cavity space is taken as free space ignoring the relatively small corrections to .lambda..sub.o for wave propagation in the cavity); EQU .GAMMA.=i(-.omega./c) [K.sub.m K.sub.e ].sup.1/2 =.alpha.+i.beta. PA1 .alpha.=real .GAMMA.=absorption coefficient, cm.sup.-1 in the lossy layer; PA1 .beta.=imag .GAMMA.=phase factor, cm.sup.-1 in the lossy layer; PA1 .lambda.=2.pi./.beta.=wavelength, cm, within the lossy layer; PA1 .omega.=2.pi.v=circular frequency, radian/sec, of the transverse electric wave (TEM); PA1 c=speed of light in vacuum=3.times.10.sup.10 cm/sec; PA1 E=E.sub.0 e(-.GAMMA.x-i.omega.t) and H=H.sub.0 e(-.GAMMA.x-i.omega.t) where, in the TEM mode, E and H are normal both to one another and to the direction of wave propagation; PA1 K.sub.e =K.sub.er +iK.sub.ei is the effective medium electric permittivity unique to each of the dielectric layers of FIG. 1 and the particulate/molecular composite lossy layer of FIG. 2. K.sub.e is defined relative to free space, and is frequency sensitive in the microwave region for materials of interest. K.sub.e is also known as the dielectric response function in accordance with the terminology of linear response theory; PA1 K.sub.m =K.sub.mr +iK.sub.mi is the effective medium magnetic permeability of the layers in FIGS. 1 and 2. K.sub.m is defined relative to free space, and is frequency sensitive in the microwave region for materials of interest. K.sub.m is also known as the magnetic response function in accordance with the terminology of linear response theory. K.sub.e and K.sub.m together are often referred to as the effective medium optical constants of the composite layer. Note that K.sub.m =1 for non-magnetic dielectric materials such as those envisioned for the application depicted in FIG. 1.
which defines the wave propagation factors in the medium:
The electric and magnetic field vectors of the propagating microwave are, respectively,
The amplitude reflection coefficient (complex number) of the structures of FIGS. 1 and 2 is: EQU R=[[(z/z.sub.o)-1]/[(z/z.sub.0)+1]] (10)
Where z=z.sub.L as given by Equation 1 for a free standing stack of two dielectric films (FIG. 1), and z is given by Equation 9 for a metal-backed dielectric film.
Power absorption in all cases is given by: EQU G(total)=P.sub.I [1-.vertline.R.vertline.(d,.omega.,K.sub.m,K.sub.e).vertline..sup.2 .vertline.[ (11)
where P.sub.I is the power density, cal/cm.sup.2 sec, incident on the film structure. In the present applications, the frequency of the microwave is fixed at that of consumer microwave ovens, approximately 2.45 GHz.
Finally, d of Equation 9 is the thickness in cm of the composite lossy layer located on the metal substrate in FIG. 2.
Two boundary conditions are next considered for a semi-transparent film (Equations 1 to 8 and FIG. 1) capable of absorbing microwave radiation. In the first condition, film 3 is replaced by free space. Calculations, using the above Equations 1, 2 and 3, provide the attenuation of the incident power density P.sub.I for various film thicknesses and the film's K.sub.e, which is the film's electric permittivity relative to free space, or its "dielectric response function" as previously defined. In the second example, film 3 is 4 cm of water where the water is fully represented by an appropriate (complex) dielectric response function. The modulation in the reflection coefficient that occurs as the thickness of the water film is increased is fairly well damped at water thicknesses greater than 2.7 cm, so that the second example emulates the use of the semi-transparent film in a package with air on the outside and a water load on the inside, like heating a cup of coffee. Again, the relevant variables are film thickness and film K.sub.e. The K.sub. e of the film can be engineered over several orders of magnitude in the values of its real and imaginary terms through choice of dielectric additives to the polymer of the film. These additives can be in molecular or particulate form. The objective of the present calculation is to learn how effective a semi-transparent film absorber may be under the two boundary conditions for all reasonable values of film thickness and K.sub.e values.
The dielectric response functions (K.sub.e) of air and water differ considerably, which produces a profound effect on the thermalization of microwave energy in the semi-transparent film. By way of example, consider the case of a free standing film loaded with a specially chosen form of particulate carbon. With free space on both sides, a maximum absorption of 28% of the incident microwave power in the film is shown to occur using Equations 1 to 3 and independently measured K.sub.e near a film thickness of 30 mil and a loading of 7 to 8 wt % carbon. Practical film thicknesses for packaging applications generally do not exceed 5 mil, for which, in this example, a maximum 10% power absorption is approached at 10% carbon loading. However, carbon loadings above 5% are judged excessive because higher loadings produce excessively high viscosity that effects processability of commercial films, and the resulting films tend to be brittle and so resist forming into packages of appropriate shapes. The calculations show that a 5% carbon film 5 mil thick with air on both sides of the film will absorb 3% of the incident power, reflect 1%, and transmit 96%. Due to the relatively high power densities generated in consumer microwave ovens, 3% power absorption can still represent a beneficial contribution to product heating. By way of comparison, calculation (Equations 8 to 11) and experiment show that the laminated foil concept in the above incorporated Fabish et al. application produces 12% power absorption in the laminate at practical film thicknesses, where "practical" means films that enable useful levels of power absorption while remaining formable into foil containers.
Similar calculation using Equations 1 to 8 for the same carbon loaded film now under the boundary conditions where 4 cm of water replaces air on the right side of the film (the "coffee cup" example) shows that the water dominates the division of power between reflection, absorption, and transmission such that 70% of the incident power is reflected for all combinations of carbon loadings and film thickness considered (0 to 12% carbon loading, 0 to 30 mil film thickness). In other words, the influence of the semi-transparent film on the heating of the load is reduced by a factor of about two thirds when the load assumes a dielectric behavior approaching that of water rather than air. Specifically, the 5% carbon, 0.0127 cm (5 mil) thick film previously discussed converts only 1% of the incident radiation into thermal energy to perform the heating function with the water load compared to 3% with air on both sides. For comparison purposes, this dramatic sensitivity of heating performance relative to the dielectric characteristics of the load does not arise with metal foil containers since the foil electrically isolates the absorbing film from the contents of the container.
The results of our consideration of semi-transparent film absorbers can be invoked to argue quite generally that little control of heating profiles of dielectric loads like foodstuffs can be expected using semi-transparent packaging films of the kind currently found in the marketplace due simply to the fact that such films control only a minor fraction of the power reaching the dielectric load for practical film compositions and thicknesses. In contrast, the foil based microwavable food package can, in principle, provide defined heating profiles for any form of load because all thermal radiation reaching the load is governed by the composite film/metal foil laminate design.
Moreover, in the above Tighe et al patents thermoplastic resins are desired as a particle binder to control to some degree particle-to-particle contact, and such control is stated to be related to a "glass transition temperature". At this temperature, the binder is said to expand so that at some point particle-to-particle contact is lost, thereby preventing further heating until the binder cools and contracts, making the particles again contiguous. However, this concept appears unsupportable in view of our previous calculations of power absorption in semi-transparent films and the fact that no known theory or experiment supports the claim that a glass transition provides volume expansion to move particles out of contact at the particulate loadings given in Column 7 of U.S. Pat. No. 4,876,423.